Integrated thermal and stress analysis for a multiple tubing completion well

ABSTRACT

A well operation simulator predicts temperature and pressure profiles of a multi-tubing completion well for well design. The simulator is comprised of modules, which when executed, determine a first set of design limits based on stress conditions arising from the temperature and pressure profiles from a multi-tubing drilling module and a multi -tubing production module for drilling and production operations. A multi-tubing multi-string module predicts the annular fluid expansion (AFE) and annular pressure buildup (APB) of the multi-tubing well from the previously calculated temperature profile, pressure profile, and stress conditions and determines a second set of design limits with the AFE/APB effects in addition to the temperature profile and pressure profile predicted from multi-tubing drilling module and multi-tubing production module. The first and second sets of design limits are depicted using one or

TECHNICAL FIELD

This disclosure generally relates to the field of earth or rock drilling and mining (E21), and to multi-tubing well design analysis.

BACKGROUND

In modern well planning and well completion design analysis, various well design factors are considered ranging from tubing configurations (single tubing, dual tubing configurations, etc.) to working fluid types (black oil hydrocarbon, vapor-liquid equilibrium modeled hydrocarbon, steam, foam, brine, synthetic fluid, compositional fluid, oil based mud, water based mud, polymer fluid, etc.). The planning process becomes more complex when the well involves various operation types (injection, circulation, production, etc.). An incorrect analysis technique that fails to correctly factor in the combination of well properties may lead to critical flaws in the final well design.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure may be better understood by referencing the accompanying drawings.

FIG. 1 depicts an example simulator diagram for thermal and stress analysis for multi-tubing completion configuration.

FIG. 2 depicts a flow chart for thermal and stress analysis for multi-tubing completion configuration.

FIG. 3 depicts a graph of an example temperature profile for a dual tubing completion with steam injection in one tubing and heavy oil production in another.

FIG. 4 depicts a graph of an example pressure profile for a dual tubing completion with steam injection in one tubing and heavy oil production in another.

FIG. 5 depicts an example Graphical User Interface (GUI) for defining the calculation for stress analysis for multi-tubing completion configuration that includes integrating a temperature profile.

FIG. 6 depicts an example GUI for loading the temperature profile from a production operation for stress analysis of well having a multi-tubing completion configuration.

FIG. 7 depicts a graph of an example safety factors plot for a casing of multi-tubing completion configuration for steam injection in one tubing and heavy oil production in another.

FIG. 8 depicts a graph of an example design limit envelope plot of a casing for a multi-tubing completion configuration for steam injection in one tubing and heavy oil production in another.

FIG. 9 depicts an example GUI for defining the temperature profiles for a multi-string stress analysis for multi-tubing completion configuration.

FIG. 10 depicts an example GUI that includes calculation of the annular fluid expansion (AFE)/annular pressure buildup (APB) for a multi-tubing completion configuration.

FIG. 11 depicts a graph of an example design limit envelope plot of a casing for a multi-tubing completion configuration from a multi-tubing tubing and casing module.

FIG. 12 depicts an example computer for thermal and stress analysis of a well design having multi-tubing completion configuration.

DESCRIPTION OF EMBODIMENTS

The description that follows includes example systems, methods, techniques, and program flows that embody aspects of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. For instance, this disclosure refers to a dual tubing configuration in illustrative examples. Aspects of this disclosure can be applied to other types of multiple tubing configuration that may utilize two or more tubings. In other instances, well-known instruction instances, protocols, structures and techniques have not been shown in detail in order not to obfuscate the description.

Overview

In modern well planning and well completion design analysis, multi-tubing completion configuration poses a unique challenge. Multi-tubing completion configuration is a configuration wherein two or more tubings are placed down a single wellbore, often arranged with packers separating different zones of a subterranean formation corresponding to each tubing. Multi-tubing completion configuration provides various advantages over a single tubing configuration, such as the ability to simultaneously perform production and injection steps in multiple well zones as well as the ability to perform accurate production allocation compared to a single tubing configuration.

Well planning and well completion design for a multi-tubing completion configuration, however, are complex and difficult to perform. The well planning and well completion design for such configurations involve considering not only various well orientations (vertical well, inclined well, directional well, and horizontal well, etc.) but also stress responses arising from the complex thermal effects of multi-tubing temperature profiles. Multi-tubing configurations include additional tubings inside the well casing that borders a shared annular fluid. The multiple tubings and the shared annular fluid require multiple heat transfer calculations each involving different heat coefficients. In multi-tubing configurations, the well tubular design carefully factors in effects arising from temperature behavior and the corresponding stress response behaviors, such as temperature effect on the trapped annulus fluid expansion (AFE) and trapped annulus pressure buildup (APB), during the life cycle of a well. The life cycle of the well includes various steps ranging from drilling operations to production operations to production enhancement workover operations. An accurate prediction of the temperature and pressure profile allows accurate subsequent design limits analysis and facilitates the design of a multi-tubing configuration well that accounts for the life cycle.

This disclosure describes a well operation simulator that can be used to predict temperature and pressure profiles of a multi-tubing completion well for well design. The multi-tubing completion well operation simulator is comprised of a combination of production, drilling, tubular casing strings and/or tubing strings (hereinafter “strings” for convenience), and multi-string program code units or software routines (hereinafter “modules” for convenience) or software sub-routines (hereinafter “sub-modules” for convenience) to simulate different aspects of a well operation on a well life cycle. When executed, the multi-tubing tubing and casing modules determine a first set of design limits based on the stress conditions arising from the temperature and pressure profiles from multi-tubing drilling module and multi-tubing production module for drilling and production operations. A multi-tubing multi-string module then predicts the AFE and APB of the multi-tubing well from the previously calculated temperature profile, pressure profile, and stress conditions and determines a second set of design limits with the AFE/APB effects in addition to the temperature profile and pressure profile predicted from multi-tubing drilling module and multi-tubing production module. The first and second sets of design limits can be depicted using one or more design limit envelope plots and safety factors plots or other plots or table of values to depict the design limitations of the well. All of the multi-tubing modules are configured to take in a set of well design parameters particular to the multi-tubing completion configuration, such as multiple fluid types and/or fluid temperatures inside each of the multiple tubings. All of the multi-tubing modules factor in the complex temperature/pressure effects that each of the multiple tubings have between one another and between various elements of the well environment.

Multi-Tubing Simulator Diagram

FIG. 1 depicts an example simulator diagram for design limits analysis for multi-tubing completion configuration. The description refers to a “multi-tubing well evaluator” or other modules/sub-modules of the multi-tubing well evaluator as performing the example operations. The moniker “multi-tubing well evaluator” is used for convenience as the operations are performed by a program or programs executed/interpreted by a device.

In FIG. 1, both a multi-tubing drilling module 102 and a multi-tubing production module 112 of the multi-tubing well evaluator obtains a predefined set of well design parameters 101. The design parameters describe a desired well environment having multi-tubing completion configuration to be simulated, wherein the well design parameters include, at least in part, formation and geothermal temperatures, wellbore casing configuration, tubing configuration, fluid configuration, and mechanical properties of the multi-tubing completion well components and the surrounding formation. The well design parameters also include parameters describing various well of differing orientations, such as vertical wells, inclined wells, directional wells, and horizontal wells.

The multi-tubing drilling module 102 simulates various drilling events and obtains associated well characteristics, such as drilling temperature and pressure conditions that are present in the well during various drilling operations, including logging, trip pipe, casing, and cementing of the operating string. The multi-tubing drilling module 102 obtains drilling operation parameters 106 that define the desired drilling events for simulation via a graphical user interface (“GUI”) of the multi-tubing drilling module 102. A thermal analyzer 104, a sub-module of the multi-tubing drilling module 102, uses the well design parameters 101 and the drilling operation parameters 106 to perform a temperature and pressure simulation 108. The thermal analyzer 104 generates the temperature and pressure profiles 110 of the well components through the simulation 108. The thermal analyzer 104 simulates the temperature and pressure conditions through heat transfer and hydraulic calculations that factor in the multiple tubings and the shared annulus. The thermal analyzer calculates the temperature of well components, including, tubings, casings, annular fluids, and annular cements. Thermal analyzer 104 calculates the pressure of components of the well, such as, fluids inside the drill-string and annular fluids. The temperature and pressure simulation 108 of the multi-tubing drilling module 102 is described in greater detail in FIG. 2. The multi-tubing drilling module passes the temperature and pressure profiles 110 to a multi-tubing multi-string module 134 of the multi-tubing well evaluator. The multi-tubing drilling module 102 also passes the temperature and pressure profiles to a multi-tubing single-string module 122 to do stress analysis for each tubing and casing string.

The multi-tubing production module 112 simulates various production events and the associated well characteristics, such as the production temperature and pressure conditions present in the well during various production operations of the well. The production operations include circulation, production, injection, gas lift and shut in operations of the operating string. The multi-tubing production module 112 obtains production operation parameters 114 defining the production event via a GUI of the multi-tubing production module 112. A thermal analyzer 116, a sub-module of the multi-tubing production module 112, uses the well design parameters 101 and the production operation parameters 114 to determine the temperature and pressure profiles 120 of the well components in a multi-tubing completion configuration well. The thermal analyzer 116 performs a temperature and pressure simulation 118 similar to that of multi-tubing production module 112 which factors in the complex thermal effects of multiple tubings and shared annular fluid in heat transfer calculations. The thermal analyzer 116 also determines the temperature of one of more components of the well, including tubings, casing, fluid in tubings, annular fluids, and annular cement, and determines the pressures of components, such as, fluids inside the tubings and annular fluids. The temperature and pressure simulation 118 of the multi-tubing production module is described in greater detail in FIG. 2. The temperature and pressure 120 profiles are passed onto the multi-tubing multi-string module 134 and the multi-tubing single-string module 122.

The multi-tubing single-string module 122 simulates stresses in the well caused by the change in the string of interest as the initial load conditions on the string change to final load conditions. The multi-tubing single-string module 122 obtains single-string (casing or tubing) parameters 126, such as the identity of the desired casing or tubing and stress load types, via a GUI of the multi-tubing single-string module 122. Using the single-string parameters 126 and the temperature and pressure profiles 120 of the multi-tubing production module, a stress analyzer 124, which is a sub-module of the multi-tubing single-string module 122, determines stress state associated with the particular stress load type and particular production operation on a casing or tubing through a stress simulation 128 from initial load condition to final load conditions. The stress simulation 128 is described in greater detail in FIG. 2. The multi-tubing single-string module 122 in turn uses the stress state 130 to generate the safety factors plot and design limit envelope plot 132. The safety factors plot and design limit envelope plot 132 may be a graphical output or it may also be a value table. The safety factors plot and design limit envelope plot 132 are two examples of plots used to perform design limits analysis. There may be other plots and analysis that convey various aspects of well design limitations. For example, one safety factors plot may depict design limitation due to safety factors, such as triaxial design factor, envelope burst design factor, envelope collapse design factor, burst design factor, and collapse design factor—other plots may depict different design factors such as burst rating and collapse rating.

The multi-tubing multi-string module 134 simulates stresses caused on one of the casings or tubings of the well system, where the well system includes all the tubing strings and casing strings, by the AFE and APB of the one or more annuli formed by their neighboring casing or tubing of the well. The multi-tubing multi-string module 134 obtains multi-string parameters 135, such as the well casing or tubing load sequence and well casing or tubing definition, via a GUI of the multi-tubing multi-string module 134. An APB/AFE analyzer 136 sub-module uses the multi-string parameters 135, the temperature and pressure profiles 110 from the multi-tubing drilling module 102, and/or the temperature and pressure profiles 120 from the multi-tubing production module 112 to determine AFE and APB for each annuli as well. The APB/AFE analyzer 136 then determines stress state 140 associated with one of the multiple casings or tubings of the well system through a stress simulation 138 that factors in the AFE and APB effect of each annulus. The stress simulation 138 is described in greater detail in FIG. 2. The multi-tubing multi-string module 134 in turn uses the stress state 140 to generate a safety factors plot and design limit envelope plot 142 or other design limitations of the well in a manner analogous to that of the multi-tubing single-string module 122.

Modifications, additions, or omissions may be made to the example diagram described in FIG. 1 without departing from the scope of the present disclosure. For example, the design limit envelope plot or safety factors plot may be replaced with other types of design limitations determined by the stress analysis. Moreover, components may be added to or removed from the diagram without departing from the scope of the present disclosure. For example, multiple sets of well design parameters may be used for the various multi-tubing modules, or graphical user interface removed and replaced with inputs from predetermined values.

Example Operation

The following flowchart illustrates in greater detail the various operations described in FIG. 1, such as the thermal and stress simulations performed. FIG. 2 depicts a flow chart for thermal and stress analysis for multi-tubing completion configuration.

At block 202, a multi-tubing well evaluator defines a set of well design parameters that are passed onto a multi-tubing production module and a multi-tubing drilling module of the multi-tubing well evaluator. The design parameters describe the well having multi-tubing completion configuration with two or more tubings inside the inner casing. In addition to the two or more tubings, the well design parameters describe the wellbore environment with the two or more tubings having a shared annular fluid.

The well design parameters that reflect the multi-tubing nature of the well serves as the basis for the complex thermal and stress analysis described in the blocks below. Any portion of the design parameters may be defined using predetermined values in literature or using in situ measurements taken in the field. The design parameters include, at least in part, formation and geothermal temperatures, wellbore casing configuration, tubing configuration, fluid configuration, and mechanical properties of the multi-tubing completion well components and the surrounding formation. The wellbore environment also includes parameters describing various orientations of the well, such as vertical well, inclined well, directional well, and horizontal well. Undisturbed temperature data from the defined set of well design parameters in block 202 may also be loaded directly into a multi-tubing multi-string module in block 226.

At block 204, a multi-tubing production module of the multi-tubing well evaluator obtains well design parameters defined at block 202 and performs operations described at blocks 206, 208, and 210. The well design parameters may be obtained before or simultaneous with the performance of any of the blocks 206, 208, and 210.

At block 206, the multi-tubing production module defines the production analysis types and parameters with multi-tubing completion configuration. Defining the production analysis types and parameters involves the multi-tubing production module obtaining production operation parameters for simulation via a GUI of the multi-tubing production module. Production operations include in part, circulation, production, injection, gas lift, shut in operations of the operating string, and other production operations.

At block 208, the multi-tubing production module simulates the temperature and pressure of the multiple tubing within the well for a production operation. The multi-tubing production module performs this simulation using a thermal analyzer. The thermal analyzer simulates the well environment, including the layout/orientation of the production tubing, flow conditions, initial annular temperature, and solves, as part of the simulation, complex heat equations describing the temperature and pressure change of the fluids inside the tubing. In simulating the temperature and pressure of the tubing, heat coefficients are determined for both tubing flow paths and heat flows, as well as the heat transfer from the tubings to the environmental rock formation through casings and annuli. Heat coefficient is a coefficient that describes the value of proportionality between the heat flux and a driving force of a heat flow, such as temperature difference between the different surfaces of tubings and casings of a well. In a multi-tubing completion configuration, temperatures may be different between outer surfaces of multiple tubings and an inner surface of the inner casing housing.

Heat transfer calculations for a multi-tubing completion configuration, including calculation of the heat coefficients, involves handling complex thermal interactions arising from the multiple tubing flow paths. For example, to solve for the heat calculations in a dual tubing environment comprised of Tubing_A, Tubing_B, inner casing, and shared annular fluid, the thermal analyzer accounts for three heat sources for the shared tubing annulus fluid. The thermal analyzer calculates one set of well components comprised of Tubing_A outer wall, shared annular fluid, and casing inner wall as one heat transfer path. The heat transfer path is comprised of two wall surface and annular fluid pairs, each with its own heat coefficient. For example, Tubing_A and its annulus fluid and an inner casing and its annulus fluid may comprise one heat transfer path. The thermal analyzer obtains the heat coefficient for the Tubing_A outer wall and annular fluid pair as coefficient h₁, and the coefficient for casing inner wall and annular fluid pair as coefficient hc₁. The thermal analyzer similarly calculates a second set of well components comprised of Tubing_B outer wall, shared annular fluid, and casing inner wall as a second heat transfer path. The second heat transfer path is comprised of two wall surface/annular fluid pair (Tubing_B/annulus fluid and inner casing/annulus fluid). The thermal analyzer obtains the heat coefficient for the Tubing_B outer wall and annular fluid pair as coefficient ho, and the coefficient for casing inner wall and annular fluid pair as coefficient hc₀. The thermal analyzer also calculates the heat coefficient for the annular fluid with the casing inner wall by calculating the average value of hc₁ and hc₀. As described above, the heat calculation for the shared annulus fluid considers two sets of heat flow paths for a dual tubing environment—in wells containing more than two tubings, the number of flow paths would increase.

The thermal analyzer, in addition to the sets of heat flow paths, calculates the heat coefficient of tubings heat transfer based on the flow properties of the respective tubing. In multi-tubing completion configuration, a well contains multiple tubing flow paths each with a different production operation. The heat coefficient calculation takes into consideration the effect on the differing heat flow inside each tubing due to the differing flow conditions. The temperature inside each of the tubing impacts the temperature of the outer walls of the tubings. For example, in a dual tubing configuration, Tubing_A may perform an injection operation whereas Tubing_B may be used to perform production. The two operations have different fluid flow properties and flow conditions affecting the temperature of the tubing differently. The thermal analyzer solves the complex heat equations of the multi-tubing configuration wells to simulate temperature and pressure simulation of the well throughout the production operations.

At block 210 the thermal analyzer determines the temperature and pressure profiles for each tubing by using temperature and pressure simulation results from block 208. The temperature profile correlates the temperature or pressure property values with respect to their measured depth (“MD”) for various components of the well, including fluids inside multiple tubings and fluid inside one or more annuli. To illustrate, FIG. 3 depicts a graph of an example temperature profile for a dual tubing completion with steam injection in one tubing and heavy oil production in another. A graph 300 of FIG. 3 charts the temperature 302 inside the multiple tubings, tubing annulus, and casing annulus with respect to the measured depth (“MD”) 304. The graph 300 illustrates the temperature profiles of Tubing A and Tubing B performing steam injection and heavy oil production. To further illustrate, FIG. 4 depicts a graph of an example pressure profile for a dual tubing completion with steam injection in one tubing and heavy oil production in another. A graph 400 of FIG. 4 charts the pressure 402 within Tubing A and Tubing B and the shared tubing annulus with respect to the MD 404.

Returning back to the flow chart of FIG. 2, at block 212 a multi-tubing drilling module of the multi-tubing well evaluator obtains the well design parameters defined at block 202 and performs operations described at blocks 213, 215 and 217. The well design parameters may be obtained before or simultaneous with the performance of any of the blocks 213, 215 and 217.

At block 213, the multi-tubing drilling module defines the drilling analysis types and parameters with multi-tubing completion configuration. The multi-tubing drilling module obtains drilling operation parameters that defines the desired drilling events for simulation via a GUI of the multi-tubing drilling module. Defined production operations may include logging, trip pipe, casing, and cementing of the operating string.

At block 215, the multi-tubing drilling module simulates the temperature and pressure of the casings within the well for a drilling operation. The multi-tubing drilling module performs the simulation using a thermal analyzer. The thermal analyzer simulates the well environment, including the layout/orientation of the casing undergoing drilling operation, flow conditions, and initial temperature of casing and annulus in a manner analogous to that described at block 208.

At block 217, the multi-tubing drilling module determines temperature and pressure profiles for each casing and its annulus. The thermal analyzer, similar to simulation at block 208, solves the complex heat equations describing the temperature and pressure change of the fluids inside the casing as part of the simulation. In simulating the final temperature and pressure of the casing, various heat coefficients are determined for both the casing flow paths and heat flows for different flow conditions, wherein instead of temperature conditions based on production operations the conditions are based on drilling operations.

At block 218, a multi-tubing single-string module of the multi-tubing well evaluator obtains the temperature and pressure profiles determined at block 210 and/or block 217. The temperature and pressure parameters profiles may be obtained before or simultaneous with the performance of any of the blocks 220.

At block 220 the multi-tubing single-string module defines the single-string (tubing or casing) analysis load types and load parameters with multi-tubing completion configuration. The multi-tubing single-string module obtains single-string (tubing or casing) parameters, such as the identity of the desired casing or tubing and the type of stress load on the single string via multiple GUI of the multi-tubing single-string module. To illustrate, FIG. 5 depicts an example GUI 500 for defining the calculation for stress analysis for multi-tubing completion configuration that includes integrating a temperature profile. The GUI 500 depicts a list 502 of available temperature and pressure profiles from block 208. Based on the temperature and pressure profile selected, an inner casing or tubing type field 504 is integratedly loaded and pre-set onto the GUI 500. An external pressure profile field 506 generates available options based on values available in literature, based on artificially generated values, or measurements obtained in situ from the field. To further illustrate, FIG. 6 depicts an example GUI for loading the temperature profile from a production operation for stress analysis of well having a multi-tubing completion configuration. A production operation field 602 correlates to the production operations of the multiple tubings previously defined. Production operations may include circulation, production, injection, gas lift, shut in operations of the operating string, and other various production operations previously defined.

Returning back to the flow chart of FIG. 2, at block 222, the multi-tubing single-string module performs a stress simulation to predict stress state of the multiple tubings within the well in a production operation or the stress state of a casing in drilling operation. The multi-tubing single-string module performs this simulation using a stress analyzer. The stress analyzer predicts the stress state of the casing or tubing defined at block 220 by solving for load equations based on the temperature profiles of each of the multiple tubings, each casing, pressure of each of the tubing flow paths, and the external pressure profile selected at block 220. The stress analyzer determines the stress on the defined casing or tubing based on the initial and final load. Further derivative stress state, such as axial safety factor, collapse and burst safety factor, may be determined using their respective algorithms. The stress analyzer in this multi-tubing single-string module performs stress analysis based on single string analysis such that the stress is analyzed with one single string, not with a system of multiple strings.

At block 224, the multi-tubing single-string module determines safety factors plot and design limit envelope plot of the string of interest. The multi-tubing single-string module obtains the stress state determined at block 222 and determine a corresponding safety factors plot and design limit envelope plot. To illustrate, FIG. 7 depicts a graph of an example safety factors plot for a casing of multi-tubing completion configuration for steam injection in one tubing and heavy oil production in another. FIG. 7 depicts a graph 700 charting American Petroleum Institute (“API”) safety factors 702 values with respect to their MD. The graph 700 depicts various safety factors 706, such as triaxial safety factor, burst safety factor, etc. To further illustrate FIG. 8 depicts a graph of an example design limit envelope plot of a casing for a multi-tubing completion configuration for steam injection in one tubing and heavy oil production in another. FIG. 8 depicts a graph 800 charting equivalent axial load 802 values of the casing with differential pressure 804. The safety envelope 806 defines the boundaries of the load and pressure differential that a string must be capable of withstanding in the well. The safety envelope 806 may vary depending on the design requirements. The load point 808 in which the load value of the casing is located outside of the safety envelope represents failure of the string to meet the well design limit. The safety factors plot and design limit envelope plot are two examples of depictions of the design limitations. There may be other plots and analysis that convey limitations in various aspects. Other plots may depict factors such as burst rating and collapse rating.

Returning back to the flow chart of FIG. 2, at block 226, a multi-tubing multi-string module of the multi-tubing well evaluator obtains the temperature and pressure profiles determined at block 210 and the temperature and pressure profile determined at block 217 as a pair of initial and final conditions. For example, temperature and pressure profiles obtained at block 210 may be the initial conditions and temperature and pressure profiles obtained at block 217 may be the final conditions. These may also be reversed such that the temperature and pressure profiles obtained at the 210 are the final conditions and the temperature and pressure profiles obtained at block 217 are the initial conditions. One or both of the temperature and pressure profiles may be obtained before or simultaneous with the performance of any of the blocks 228. The undisturbed temperature may also be used as initial condition temperature.

At block 228 the multi-tubing multi-string module defines the strings analysis load types and parameters with multi-tubing completion configuration. The multi-tubing multi-string module obtains multi-string parameters, such as the well casing or tubing load sequence and desired well casing or tubing definition via a GUI of the multi-tubing multi-string module. To illustrate, FIG. 9 depicts an example GUI for defining the temperature profiles for a multi-string stress analysis for multi-tubing completion configuration. FIG. 9 depicts a GUI 900 that includes a casing or tubing string list field 902 that has multiple available casing or tubing in a multi-tubing configuration well. The temperature profiles are integratedly loaded to the multi-tubing multi-string module based on the final operation 904 of the multiple tubings selected, for example steam injection in one tubing and heavy oil production in the other. The undisturbed temperature is selected as an initial condition 906.

Returning back to the flow chart of FIG. 2, at block 230, the multi-tubing multi-string module determines the AFE and APB of the one or more annuli in between each neighboring-casing pairs of the well and performs a stress simulation to predict stresses placed on one of the multiple casing or tubing of the well. The multi-tubing multi-string module accounts for the effects arising from the multiple casings of the well and the effect that they have on one another, not just one isolated casing. The multi-tubing multi-string module determines the AFE and APB using an AFE/APB analyzer. In determining the AFE and APB, the AFE/ABP analyzer may use any number of AFE/APB modeling algorithms. The AFE/APB analyzer solves for the AFE and ABP for each annulus by modeling the AFE and APB based on the multi-string parameters defined at block 228, based on the temperature and pressure profiles from the multi-tubing drilling module determined at block 217 and/or block 210 based on the temperature and pressure profiles from the multi-tubing production module at block 210. To illustrate, FIG. 10 depicts an example GUI that includes calculation of the annular fluid expansion (AFE)/ annular pressure buildup (APB) for a multi-tubing completion configuration. FIG. 10 depicts a GUI 1000 that depicts a table. The table includes multiple columns, including a string annulus column 1006. The string annulus column 1006 lists five different configurations of string annulus, which are the annulus of each casings of the well. The tables also include an AFE Pressure column 1002 and AFE Volume column 1004. The AFE Pressure column 1002 indicates the calculated pressure change caused by the AFE phenomenon for each of the string annulus configurations. The AFE Volume column 1004 indicates the calculated volume change caused by the AFE effect for each of the string annulus configurations.

Returning back to the flow chart of FIG. 2, at block 230 the AFE/APB analyzer then applies internal and external pressure of a casing or tubing of the well as identified in each of the pressure profiles, to do further stress analysis on each casing or tubing. In a stress analysis of a multi-string well, all the casings or tubings may potentially affect one another. For example, the fluid expansion on one of the casings or tubings may result in subsequent stretching on others. AFE/APB analyzer factors in the effect the casings or tubings have on one another, including the inner casing housing the multiple tubings.

The annular pressure buildup (APB) in one casing or tubing may result in additional stress on each of the casings or tubings as well as result in wellhead movement. The AFE/APB analyzer predicts the stress state of the desired casings or tubings of the multiple casings or tubings from block 228 of the well system by solving for load equations based on the temperature and pressure profiles and the AFE/APB of each annuli. Further derivative stress safety factors, such as axial safety factor, collapse and burst safety factor, may be determined using their respective algorithms with the effects of APB/AFE.

At block 232, the multi-tubing single-string module determines casing and tubing safety factors plot and design limit envelope plot of the strings of the well with the effect of the APB/AFE and inter-string interaction in the multi-string well system from block 230. The casing and tubing safety factors plot and design limit envelope plot may alternatively be a data table. The stress state determined at block 230 in turn are to determine the design limit envelope plot or other design limitations plot of the well. To illustrate, FIG. 11 depicts a graph of an example design limit envelope plot of a casing for a multi-tubing completion configuration from a multi-tubing single-string module. FIG. 11 depicts a graph 1100 charting equivalent axial load 1102 values with differential pressure 1104 of a casing having multi-tubing completion configuration. The safety envelope 1106 defines the boundaries of the load and pressure differential that a well must be capable of withstanding. The safety envelope 1106 may vary depending on the design requirements. For the production tieback 1108, its load falls outside of the safety envelop and therefore would not meet the design requirements.

Modifications, additions, or omissions may be made to the example flow chart described in FIG. 2 without departing from the scope of the present disclosure. For example, the design limit envelope plot or safety factors plot may be replaced with other types of design limitations determined by the stress state. Moreover, components may be added to or removed from the flow chart without departing from the scope of the present disclosure.

Example Computer

FIG. 12 depicts an example computer for thermal and stress analysis of a well design having multi-tubing completion configuration. The computer includes a processor 1201 (possibly including multiple processors, multiple cores, multiple nodes, and/or implementing multi-threading, etc.). The computer includes memory 1207. The memory 1207 may be system memory (e.g., one or more of cache, static random access memory (SRAM), dynamic random access memory (DRAM), Twin Transistor RAM, enhanced dynamic random access memory (eDRAM), extended data output (EDO) RAM, double data rate (DDR) RAM, electrically erasable programmable read-only memory (EEPROM), nano-random access memory (NRAM), resistive random access memory (RRAM), silicon-oxide-nitride-oxide-silicon (SONOS), parameter random access memory (PRAM), etc.) or any one or more of the above already described possible realizations of machine-readable media. The computer system also includes a bus 1203 (e.g., peripheral component interconnect (PCI), industry standard architecture (ISA), PCI-Express, HyperTransport® bus, InfiniBand® bus, NuBus, etc.) and a network interface 1205 (e.g., a Fiber Channel interface, an Ethernet interface, an internet small computer system interface, synchronous optical networking (SONET) interface, wireless interface, etc.).

The computer also includes a multi-tubing well evaluator 1211. The multi-tubing well evaluator 1211 can simulate temperature and pressure profiles of a multi-tubing completion well, simulates stresses in the casing or tubing of multi-tubing completion well, determine the AFE and APB of a multi-tubing completion well, among other simulations, calculations, and operations described above. Any one of the previously described functionalities may be partially (or entirely) implemented in the hardware and/or on the processor 1201. For example, the functionality may be implemented with an application specific integrated circuit, in logic implemented in the processor 1201, in a co-processor on a peripheral device or card, etc. Further, realizations may include fewer or additional components not illustrated in FIG. 12 (e.g., video cards, audio cards, additional network interfaces, peripheral devices, etc.). The processor 1201 and the network interface 1205 are coupled to the bus 1203. Although illustrated as being coupled to the bus 1203, the memory 1207 may be coupled to the processor 1201.

It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by program code. The program code may be provided to a processor of a general purpose computer, special purpose computer, or other programmable machine or apparatus for execution to implement the various methods described above. As will be appreciated, aspects of the disclosure may be embodied as a system, method or program code/instructions stored in one or more machine-readable media. Accordingly, aspects may take the form of hardware, software (including firmware, resident software, micro-code, etc.), or a combination of software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” The functionality presented as individual modules/units in the example illustrations can be organized differently in accordance with any one of platforms (operating system and/or hardware), application ecosystems, interfaces, programmer preferences, programming language, administrator preferences, etc.

Any combination of one or more machine readable medium(s) may be utilized. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable storage medium may be, for example, but not limited to, a system, apparatus, or device, that employs any one of or combination of electronic, magnetic, optical, electromagnetic, infrared, or semiconductor technology to store program code. More specific examples (a non-exhaustive list) of the machine-readable storage medium would include the following: a portable computer diskette, a hard disk, a RAM, a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a machine-readable storage medium may be any tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. A machine-readable storage medium is not a machine-readable signal medium.

A machine-readable signal medium may include a propagated data signal with machine readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A machine-readable signal medium may be any machine-readable medium that is not a machine-readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a machine-readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as the Java® programming language, C++ or the like, a dynamic programming language such as Python, a scripting language such as Perl programming language or PowerShell script language, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on a stand-alone machine, may execute in a distributed manner across multiple machines, and may execute on one machine while providing results and or accepting input on another machine.

The program code/instructions may also be stored in a machine-readable medium that can direct a machine to function in a particular manner, such that the instructions stored in the machine-readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

Using the apparatus, systems, and methods disclosed herein may facilitates in the design of a multi-tubing configuration well that accounts for the life cycle.

While the aspects of the disclosure are described with reference to various implementations and exploitations, it will be understood that these aspects are illustrative and that the scope of the claims is not limited to them. In general, techniques for simulating or determining properties of the multi-tubing completion wells as described herein may be implemented with facilities consistent with any hardware system or hardware systems. Many variations, modifications, additions, and improvements are possible.

Plural instances may be provided for components, operations, or structures described herein as a single instance. Finally, boundaries between various components, operations, and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of the disclosure. In general, structures and functionality presented as separate components in the example configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the disclosure.

Use of the phrase “at least one of” preceding a list with the conjunction “and” should not be treated as an exclusive list and should not be construed as a list of categories with one item from each category, unless specifically stated otherwise. A clause that recites “at least one of A, B, and C” can be infringed with only one of the listed items, multiple of the listed items, and one or more of the items in the list and another item not listed.

EXAMPLE EMBODIMENTS

A method comprises simulating a production operation for a described well with multiple tubings to determine a production temperature profile and a production pressure profile for the described well based on a flow path of each tubing, shared annulus fluid, and tubing surface-based heating coefficient of each tubing. For each of the multiple tubings, a production pressure profile and a production temperature profile are determined based, at least in part, on the production and temperature profiles for the described well. A stress simulation is performed based on the production temperature and pressure profiles of the multiple tubings to predict stress state of the well. A first set of design limitations of the well is determined based on the predicted stress state of the multiple tubings and/or casings. A drilling operation for the described well is simulated to determine a drilling temperature profile and a drilling pressure profile for the described well. A trapped annular pressure buildup property and a trapped annular fluid expansion property are determined for each annulus in a plurality of annuli located between an inner string and one or more outer casings of the well based on the temperature and pressure profiles. A second set of design limitations of the well is determined with the effects of the trapped annular pressure buildup conditions and the trapped annular fluid expansion conditions.

Determining temperature and pressure profiles of the elements of the well further comprises obtaining heat coefficients between each of the multiple production tubings and the tubing annular fluid. Determining temperature and pressure profiles of the elements of the well further comprises obtaining heat coefficients between a casing surrounding the multiple production tubings and the tubing annular fluid. Simulating multi-tubing heat flow is based on heat flow associated with same or different tubing flow conditions inside the production tubings. Determining temperature and pressure profiles comprises determining temperature profiles of the production tubings, a casing, and fluids inside the plurality of annulus, and determining pressure profiles of the fluids inside the plurality of annulus. Determining the first set of design limitations at least includes determining a safety factors plot or value and/or a design limit envelope plot or value of one of the strings. Determining the second set of design limitations at least includes determining a design limit envelope one of the strings of the well.

A system comprises a processor and a machine-readable medium having instructions stored thereon that are executable by the processor to cause the system to generate temperature and pressure profiles of elements of a well comprising multiple production tubings based on a set of well design parameters. The instructions to generate the temperature and pressure profiles comprise instructions to simulate multi-tubing heat flow and to simulate interactions amongst at least a tubing annulus fluid shared by multiple production tubings, each of the multiple production tubings, and an inner tubular string containing the multiple production tubings within.

The instructions further comprise instructions to determine a first set of design limitations of the well based on the temperature and pressure profiles of the elements of a well and instructions to determine a trapped annular pressure buildup property and a trapped annular fluid expansion property for each annulus in a plurality of annuli located between an inner string and one or more outer casings of the well based on the temperature and pressure profiles, and instructions to determine a second set of design limitations of the well with the effects of the trapped annular pressure buildup conditions and the trapped annular fluid expansion conditions.

The instructions to generate temperature and pressure profiles of the elements of the well further comprises instructions to obtain heat coefficients between each of the multiple production tubings and the tubing annular fluid. The instructions to generate temperature and pressure profiles of the elements of the well further comprise instructions to obtain heat coefficients between a casing surrounding the multiple production tubings and the tubing annular fluid. The instructions to simulate multi-tubing heat flow are based on heat flow associated with different tubing flow conditions inside the production tubings. The instructions to determine temperature and pressure profiles comprise instructions to determine temperature profiles of the production tubings, a casing, and fluids inside the plurality of annulus, and instructions to determine pressure profiles of the fluids inside the plurality of annulus. The instructions to determine the first set of design limitations at least include instructions to determine a safety factors plot or value, and/or a design limit envelope plot or value of one of the strings. The instructions to determine the second set of design limitations at least include instructions to determine a design limit envelope plots of the well.

A non-transitory, computer-readable medium has instructions stored thereon that are executable by a computing device to perform operations comprising generating temperature and pressure profiles of elements of a well comprising multiple production tubings based on a set of well design parameters. Generating the temperature and pressure profiles comprises simulating multi-tubing heat flow and simulating interactions amongst at least a tubing annulus fluid shared by multiple production tubings, each of the multiple production tubings, and an inner tubular string containing the multiple production tubings within. The operations further comprise determining a first set of design limitations from stress analysis of the well based on the temperature and pressure profiles of the elements of a well, determining a trapped annular pressure buildup property and a trapped annular fluid expansion property for each annulus in a plurality of annuli located between an inner string and one or more outer casings of the well based on the temperature and pressure profiles, and determining a second set of design limitations of the well with the effects of the trapped annular pressure buildup conditions and the trapped annular fluid expansion conditions.

Generating temperature and pressure profiles of the elements of the well further comprises obtaining heat coefficients between each of the multiple production tubings and the tubing annular fluid. Generating temperature and pressure profiles of the elements of the well further comprises obtaining heat coefficients between a casing surrounding the multiple production tubings and the tubing annular fluid. Simulating multi-tubing heat flow is based on heat flow associated with different tubing flow conditions inside the production tubings. Determining temperature and pressure profiles comprises determining temperature profiles of the production tubings, a casing, and fluids inside the plurality of annulus, and determining pressure profiles of the fluids inside the plurality of annulus. Determining the first set of design limitations at least includes determining a safety factors plot or value and a design limit envelope plot or value of one of the strings. 

What is claimed is:
 1. A method comprising: simulating a production operation for a described well with multiple tubings to determine a production temperature profile and a production pressure profile for the described well based on a flow path of each tubing, shared annulus fluid, and tubing surface-based heating coefficient of each tubing; for each of the multiple tubings, determining a production pressure profile and a production temperature profile based, at least in part, on the production and temperature profiles for the described well; performing a stress simulation based on the production temperature and pressure profiles of the multiple tubings to predict stress state of the described well; determining a first set of design limitations of the described well based on: the predicted stress state of the multiple tubings, one or more casings of the described well, or combinations thereof; simulating a drilling operation for the described well to determine a drilling temperature profile and a drilling pressure profile for the described well; determining a trapped annular pressure buildup property and a trapped annular fluid expansion property for each annulus in a plurality of annuli located between an inner string and one or more outer casings of the described well based on the temperature and pressure profiles; and determining a second set of design limitations of the described well with the effects of the trapped annular pressure buildup conditions and the trapped annular fluid expansion conditions.
 2. The method of claim 1, wherein determining temperature and pressure profiles of the multiple tubings of the described well further comprises obtaining heat coefficients between each of the multiple production tubings and a tubing annular fluid.
 3. The method of claim 2, wherein determining temperature and pressure profiles of the multiple tubings of the described well further comprises obtaining heat coefficients between a casing surrounding the multiple production tubings and the tubing annular fluid.
 4. The method of claim 1, wherein simulating multi-tubing heat flow is based on heat flow associated with same or different tubing flow conditions inside the production tubings.
 5. The method of claim 1, wherein determining temperature and pressure profiles comprises determining temperature profiles of the production tubings, a casing, and fluids inside the plurality of annulus, and determining pressure profiles of the fluids inside the plurality of annulus.
 6. The method of claim 1, wherein determining the first set of design limitations at least includes determining: a safety factors plot, a safety factors value, a design limit envelope plot of one of the strings, a design limit envelope value of one of the strings, or combinations thereof
 7. The method of claim 1, wherein determining the second set of design limitations at least includes determining a design limit envelope one of the strings of the described well.
 8. A system comprising: a processor; and a machine-readable medium having instructions stored thereon that are executable by the processor to cause the system to, generate temperature and pressure profiles of elements of a well comprising multiple production tubings based on a set of well design parameters, wherein the instructions to generate the temperature and pressure profiles comprise instructions to simulate multi-tubing heat flow and to simulate interactions amongst at least a tubing annulus fluid shared by multiple production tubings, each of the multiple production tubings, and an inner tubular string containing the multiple production tubings within, to determine a first set of design limitations of the well based on the temperature and pressure profiles of the elements of a well; to determine a trapped annular pressure buildup property and a trapped annular fluid expansion property for each annulus in a plurality of annuli located between an inner string and one or more outer casings of the well based on the temperature and pressure profiles; and to determine a second set of design limitations of the well with the effects of the trapped annular pressure buildup conditions and the trapped annular fluid expansion conditions.
 9. The system of claim 8, wherein the instructions to generate temperature and pressure profiles of the elements of the well further comprise instructions to obtain heat coefficients between each of the multiple production tubings and a tubing annular fluid.
 10. The system of claim 9, wherein the instructions to generate temperature and pressure profiles of the elements of the well further comprise instructions to obtain heat coefficients between a casing surrounding the multiple production tubings and the tubing annular fluid.
 11. The system of claim 8, wherein the instructions to simulate multi-tubing heat flow are based on heat flow associated with different tubing flow conditions inside the production tubings.
 12. The system of claim 8, wherein the instructions to determine temperature and pressure profiles comprise instructions to determine temperature profiles of the production tubings, a casing, and fluids inside the plurality of annulus, and instructions to determine pressure profiles of the fluids inside the plurality of annulus.
 13. The system of claim 8, wherein the instructions to determine the first set of design limitations at least include instructions to determine a safety factors plot, a safety factors value, a design limit envelope plot of one of the strings, a design limit envelope value of one of the strings, or combinations thereof
 14. The system of claim 8, wherein the instructions to determine the second set of design limitations at least include instructions to determine a design limit envelope plot of the well.
 15. A non-transitory, computer-readable medium having instructions stored thereon that are executable by a computing device to perform operations comprising: generating temperature and pressure profiles of elements of a well comprising multiple production tubings based on a set of well design parameters, wherein generating the temperature and pressure profiles comprises simulating multi-tubing heat flow and simulating interactions amongst at least a tubing annulus fluid shared by multiple production tubings, each of the multiple production tubings, and an inner tubular string containing the multiple production tubings within; determining a first set of design limitations from stress analysis of the well based on the temperature and pressure profiles of the elements of the well; determining a trapped annular pressure buildup property and a trapped annular fluid expansion property for each annulus in a plurality of annuli located between an inner string and one or more outer casings of the well based on the temperature and pressure profiles; and determining a second set of design limitations of the well with the effects of the trapped annular pressure buildup conditions and the trapped annular fluid expansion conditions.
 16. The non-transitory, computer-readable medium of claim 15, wherein generating temperature and pressure profiles of the elements of the well further comprises obtaining heat coefficients between each of the multiple production tubings and a tubing annular fluid.
 17. The non-transitory, computer-readable medium of claim 16, wherein generating temperature and pressure profiles of the elements of the well further comprises obtaining heat coefficients between a casing surrounding the multiple production tubings and the tubing annular fluid.
 18. The non-transitory, computer-readable medium of claim 15, wherein simulating multi-tubing heat flow is based on heat flow associated with different tubing flow conditions inside the production tubings.
 19. The non-transitory, computer-readable medium of claim 15, wherein determining temperature and pressure profiles comprises determining temperature profiles of the production tubings, a casing, and fluids inside the plurality of annulus, and determining pressure profiles of the fluids inside the plurality of annulus.
 20. The non-transitory, computer-readable medium of claim 15, wherein determining the first set of design limitations at least includes determining a safety factors plot, a safety factors value, a design limit envelope plot of one of the strings, a design limit envelope value of one of the strings, or combinations thereof. 